jmc

First, we can factor out $1000=10^3$, so $\sqrt[3]{2744000}=10\sqrt[3]{2744}$. To proceed, we can take out factors of two from 2744, to find that $2744=2\cdot 1372=2\cdot 2\cdot 686=2^3\cdot 343$. With a little bit of guess and check, notice that $7^3=343$. Therefore, $10\sqrt[3]{2744}=10(14)=\boxed{140}$.